Apologising when things have gone wrong is an important part of handling complaints effectively. It is often the first step to repairing a damaged relationship and, while apologising cannot change what has happened, it can help to restore dignity and trust.
A meaningful apology can help both sides calm their emotions and move on to put things right. If communicated sincerely and effectively, it can undo the negative effects of previous service failings, in addition to allowing service providers to acknowledge a failing that may otherwise have continued to affect customers in the future.
The Scottish Public Services Ombudsman (SPSO) has produced guidance outlining what you need to do to make a meaningful apology: SPSO Guidance on Apology (PDF, 54KB)
You may also be interested in an article by Dr Dorothy Armstrong, Nursing Advisor to SPSO, on the Power of Apology.